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## Singularly perturbed advection-diffusion-reaction problems : Comparison of operator-fitted methods

Kavčič, Iva; Rogina, Mladen; Bosner, Tina
Singularly perturbed advection-diffusion-reaction problems : Comparison of operator-fitted methods // Mathematics and computers in simulation, 81 (2011), 10; 2215-2224 doi:10.1016/j.matcom.2010.12.029 (međunarodna recenzija, članak, znanstveni)

Naslov
Singularly perturbed advection-diffusion-reaction problems : Comparison of operator-fitted methods

Autori
Kavčič, Iva ; Rogina, Mladen ; Bosner, Tina

Izvornik
Mathematics and computers in simulation (0378-4754) 81 (2011), 10; 2215-2224

Ključne riječi
Singular perturbations; boundary layers; collocation; difference schemes; exponential splines

Sažetak
We compare classical methods for singular perturbation problems, such as El-Mistikawy and Werle scheme and its modifications, to exponential spline collocation schemes. We discuss subtle differences that exist in applying this method to one dimensional reaction-diffusion problems and advection-diffusion problems. For pure advection-diffusion problems, exponential tension spline collocation is less capable of capturing only one boundary layer, which happens when no reaction term is present. Thus the existing collocation scheme in which the approximate solution is a projection to the space piecewisely spanned by $\{; ; ; ; 1, x, \exp{; ; ; ; \left(\pm p x\right)}; ; ; ; \}; ; ; ;$ is inferior to the generalization of El-Mistikawy and Werle method proposed by Ramos. We show how to remedy this situation by considering projections to spaces locally spanned by $\{; ; ; ; 1, x, x^{; ; ; ; 2}; ; ; ; , \exp{; ; ; ; \left(p x\right)}; ; ; ; \}; ; ; ;$, where $p>0$ is a tension parameter. Next, we exploit a unique feature of collocation methods, that is, the existence of special collocation points which yield better global convergence rates and double the convergence order at the knots.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika, Geologija

Napomena
Rad je prezentiran na skupu The 3rd International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources (MAMERN 2009).

Projekt / tema
037-1193086-2771 - Numeričke metode u geofizičkim modelima (Saša Singer, )

Ustanove
Prirodoslovno-matematički fakultet, Zagreb

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

• Zentrallblatt für Mathematik/Mathematical Abstracts